Raíces unitarias y ciclos en las principales variables macroeconómicas de argentina

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1 Raíces uniarias y ciclos en las principales variables macroeconómicas de argenina Jorge Eduardo Carrera, Mariano Féliz 2 y Demian Tupac Panigo 3 Documeno de Trabajo Nro. 2 Febrero 2 CACES-UBA, UNLP 2 CACES-UBA, PIETTE-CONICET, UNLP 3 CACES-UBA, PIETTE-CONICET, UNLP

2 RAÍCES UNITARIAS Y CICLOS EN LAS PRINCIPALES VARIABLES MACROECONÓMICAS DE ARGENTINA Jorge Eduardo Carrera (CACES-UBA, UNLP) Mariano Féliz 2 (CACES-UBA, PIETTE-CONICET, UNLP) Demian Tupac Panigo 3 (CACES-UBA, PIETTE-CONICET, UNLP) Firs draf: Augus 999. This version: January 2. Resumen En ese rabajo esudiamos las propiedades de inegración de algunas de las principales variables macroeconómicas de Argenina. Presenamos una meodología robusa para el análisis de persisencia frene a los shocks que afecan a las variables macroeconómicas y sus consecuencias sobre la esimación del componene cíclico y del componene endencial. Nuesra esraegia consisen en esear la esacionariedad de las series uilizando una secuencia de indicadores de forma de analizar el problema desde res punos de visa convergenes: Persisencia de las series, Raíz Uniaria y Raíz Uniaria con Quiebre Esrucural, buscando obener resulados robusos respeco a las propiedades de inegración de 4 de las principales variables macroeconómicas argeninas. De esa manera logramos clasificar a las series en cuaro grupos homogéneos de acuerdo con su orden de inegración. Eso nos permie deerminar la mejor esraegia a seguir para la esimación del componene cíclico de cada variable. Por ejemplo, enconramos que el PBI puede ser robusamene considerado como inegrado de primer orden, I(). Keywords: Uni Roo, Persisence, Cycles, Srucural breaks, Argeninean Macroeconomic variables JEL Classificaion Numbers: C3, C5, E3 [email protected] 2 [email protected] 3 [email protected]

3 UNIT ROOTS AND CYCLES IN THE MAIN MACROECONOMIC VARIABLES FOR ARGENTINA Jorge Eduardo Carrera 4 (CACES-UBA, UNLP) Mariano Féliz 5 (CACES-UBA, PIETTE-CONICET, UNLP) Demian Tupac Panigo 6 (CACES-UBA, PIETTE-CONICET, UNLP) Firs draf: Augus 999. This version: January 2. Absrac In his paper we sudy he inegraion properies of some of he main macroeconomic series of Argenina. We presen a robus mehodology for he analysis of persisence of shocks affecing macroeconomic series and is consequences on he modeling of he cyclical and permanen componens. Our sraegy consiss on esing he saionariy of he series by using a sequence of indicaors in such a way ha we can analyze he problem from hree converging poins of view: Persisence of he series, Uni Roo (UR) and UR wih a Srucural Breaks, hus reaching robus resuls regarding he inegraion properies of he main 4 Argeninean macroeconomic ime series. We are able o classify hem in four homogenous groups according o is order of inegraion. This allows us o deermine he bes sraegy for modeling he cyclical componen of each variable. For example, we found ha he GDP can be robusly considered inegraed of order one, I (). Keywords: Uni Roo, Persisence, Cycles, Srucural breaks, Argeninean Macroeconomic variables JEL Classificaion Numbers: C3, C5, E3 4 [email protected] 5 [email protected] 6 [email protected]

4 UNIT ROOTS AND CYCLES IN THE MAIN MACROECONOMIC VARIABLES FOR ARGENTINA Jorge Eduardo Carrera (CACES-UBA, UNLP) Mariano Féliz 2 (CACES-UBA, PIETTE-CONICET, UNLP) Demian Tupac Panigo 3 (CACES-UBA, PIETTE-CONICET, UNLP) Firs draf: Augus 999. This version: January 2. I. CYCLE, TREND AND THE DATA GENERATING PROCESS... I.A. DGP AND THE ORDER OF INTEGRATION... 2 I.B. SIMPLE MEASURES OF PERSISTENCE... 3 I.B.. Firs order auocorrelaion coefficien (FOAC). A recursive and rolling approach I.B.2. Relaive persisence measure (RPM)... 3 I.C. TEST OF UNIT ROOTS... 4 I.D. ROLLING AND RECURSIVE ADF TEST FOR UNIT ROOT... 5 I.E. VARIANCE RATIO MEASUREMENT (VR)... 5 I.F. UNIT ROOT UNDER THE HYPOTHESIS OF A STRUCTURAL BREAK... 6 I.G. A SYNTHESIS OF THE DIFFERENT VIEWS... 8 I.H. THE METHODOLOGY... 9 I.I. THE DATA... II. MEASURES OF THE PERSISTENCE OF THE MACROECONOMIC SERIES IN ARGENTINA... II.A. THE CYCLE... II.B. WHAT CYCLE?... II.C. SIMPLE MEASURES OF PERSISTENCE... II.C.. Firs order correlaion coefficiens (FOAC)... II.C.2. Relaive persisence measure (RPM)... 2 II.D. UNIT ROOT TESTS... 2 II.D.. Augmened Dickey-Fuller (ADF) and Phillips-Perron (PP)... 2 II.D.2. Recursive and Rolling Augmened Dickey-Fuller... 3 II.E. VARIANCE RATIO TEST (VR)... 4 II.F. UNIT ROOT TESTS UNDER STRUCTURAL BREAK... 4 II.F.. Perron uni roo es wih exogenous srucural break... 4 II.F.2. Perron uni roo es wih endogenous srucural break... 5 III. A COMPARATIVE ANALISYS... 6 IV. CONCLUSIONS... 7 V. REFERENCES... 8 VI. FIGURES AND TABLES...2 [email protected] 2 [email protected] 3 [email protected]

5 UNIT ROOTS AND CYCLES IN THE MAIN MACROECONOMIC VARIABLES FOR ARGENTINA Jorge Eduardo Carrera (CACES-UBA, UNLP) Mariano Féliz 2 (CACES-UBA, PIETTE-CONICET, UNLP) Demian Tupac Panigo 3 (CACES-UBA, PIETTE-CONICET, UNLP) Firs draf: Augus 999. This version: January 2. I. CYCLE, TREND AND THE DATA GENERATING PROCESS The cycle is very imporan for macroeconomic heory and for economic policy. Since he 8s here has exised srong conroversy as o wheher he Real Business Cycle models are he mos appropriae framework o explain he evoluion of he economies. Thus here s been dispue as o he role of real and moneary (nominal) shocks in he shor and long run economic performance. This relaes o he fac ha if shocks are mainly ransiory hen sabilizaion policies have a reason o be while if shocks are persisen he mos appropriae policies are srucural ones. The quesions we consider relevan in his conex and ha we will ry o answer (albei parially) in his work cenering our aenion on he Argeninean economy are: a) Wha is he imporance and size of he cycle in Argenina for he mos relevan series? b) Wha is he srucure of shocks hiing he economy like? Are shocks ransiory or permanen? How persisen are hey? c) Wha is he bes sraegy o model he cycle in erms of he de-rending mehod o be used? d) Wha is he effeciveness of sabilizaion policies? e) Was he converibiliy a srucural change ha modified he behavior of he series? f) How much does shock persisence maer o forecas he fuure behavior of a series? For any discussion on he cycle i is cenral o be able o measure i. Tha is, i is of grea imporance o define wha is he acual objec being sudied. Differen ways of measuring he cycle will give us very differen esimaions as regards is imporance. As a maer of fac, i is possible ha he cycle doesn exiss a all (Cribari-Neo, 996). When we exrac he cycle from a ime series (y ) a firs sep is o deermine which is he permanen componen (y p ) of he series and which is he cyclical one (C ). The permanen componen is associaed wih he rend ha he series is supposed o follow in he long run and he cycle wih he saionary deviaions. Thus he cycle is consruced as follows: C = y - y p () The fundamenal problem appears when we need o esablish he characerisics of he permanen componen. Till he appearance of Box and Jenkins (97) mehodology, saionary serially correlaed deviaions around a deerminisic rend where he paradigm. Since hen, aenion has moved oward ARIMA 4 models ha allow working flexibly wih any kind of series, being hem saionary or no. [email protected] 2 [email protected] 3 [email protected] 4 Auoregressive model, inegraed wih moving averages.

6 This changed he way of deermining and measuring he cycle since i mean moving from he generalized use of deerminisic rends (in paricular linear rends where he mos common assumpion when calculaing he cycle) o sochasic rend specificaions. To be able o know wha he mos appropriae rend is, he firs hing o do is o go back o he Daa Generaing Process (DGP). According o he srucure of he DGP ha bes fis each series we ll esablish he kind of rend ha should be used for each one. The DGP is hus crucial for he decomposiion beween rend and cycle and hus for he deerminaion of he duraion and ampliude of he cyclical flucuaions in each macroeconomic variable. I.A. DGP and he order of inegraion A series ha needs o be differeniaed k imes o acquire saionariy is considered o be inegraed of order k: I (k) For example, a series as follows: y = α +ρy - + ε (2) given ha ε is i.i.d., when ρ = is non-saionary. This is known as a Random Walk wih drif process 5. The series urns ino a saionary one when i is differeniaed (in he case of equaion 2 only once), so he daa generaing process of his series is said o be a difference-saionary process (DSP). This kind of series is also said o presen sochasic non-saionariy (Charenza, 997) and can be adequaely modeled as a Uni Roo process (URP) in he auoregressive erms. Nelson and Plosser (982) in heir pioneering work for he Unied Saes show ha 3 of he 4 macroeconomic series hey sudied presen sochasic non-saionariy, specifically ha hey are I (), ha is hey have a sochasic rend and hus are o be modeled as Uni Roo processes. However, when he series is of he kind: y = α + δ + ε wih ε i i.i.d.~n(,σ 2 ) (3) y is a saionary series around a deerminisic rend. Saionariy is achieved when by subracing he deerminisic componen (in equaion 3, α + δ) from y. The process behind his kind of series is called a rend-saionary process (TSP). This is an I () series, so i doesn need o be differeniaed o make i saionary. This was he radiional way of reaing series ill Nelson and Plosser s work came around. Maddala and Kim (998) sae ha from he numerous empirical works in exisence i is eviden ha he deerminisic rend is mos common amongs real raher han nominal variables. In a TSP he effec of shocks vanishes in he long run when moves farher away from he momen of he shock. Wih DSP he effec of he shock remains. This is wha s behind he idea of persisence of innovaions. A sochasic rend implies ha each shock is permanen and changes he long run rend. Since he variance grows wihou limi, forecasing is made difficul in his kind of series, in comparison wih rend-deerminisic series where he variance is limied by he variance of errors and hus forecasing can be based on he rend. A similar shock has differen effecs depending on wheher he process is saionary or no; simplifying, I () or I (). Then for a process where ρ = in period we have: y = y - + ε (4) in + y + = y + ε +, subsiuing, we have: y + = y - + ε + ε + (5) The effec of he shock in ε ranspors and persiss in he following sub-periods indefiniely. 5 I should be noed ha when y is a RW wih drif conains a deerminisic rend. In (2) he consan α can be inerpreed as he deerminisic rend. Suppose he value y = y en = ; subsiuing repeaedly: + ε i i= y = α + y wih ε i i.i.d.~n(,σ 2 ) hus he consan α in his I() process represens a linear deerminisic rend. 2

7 If he series is saionary I () wih ρ < in period, we have: y = ρy - + ε (6) in + y + = ρy + ε +, subsiuing, we ge: y + = ρ 2 y - + ρε + ε + (7) The effec of he shock slowly disappears, wih greaer velociy he lower he value of ρ. Then, shocks have no persisence so hey can be considered ransiory. Anoher way of expressing he same is o sae ha he cenral disincion o deermine wheher he rend is sochasic or deerminisic is o verify if he series reurns o is deerminisic rend (or mean in he case here is no rend), a leas in a reasonable period of ime. This, of course, relaes o he persisence of innovaions. An I () series is equivalen o he accumulaion of shocks and no underlying force exiss in he behavior of he series ha will make i reurn o is mean sysemaically. Making a misake in he deerminaion of he DGP could ake o imporan errors. If he series is a TSP and we differeniae we are over-differeniaing he series, and if he original series is a DSP and we rea i as a TSP when running he regression agains ime we are underdiffereniaing. However, Plosser and Schwer (978) sae ha he risk of over-differeniaing is no as grea if we analyze carefully he properies of he residuals of he regression. A cenral poin, made by Nelson and Kang (98), is ha if he rue daa generaing process is a DSP and we exrac he rend reaing i as a series wih a TSP, hen he cycle will exhibi spurious periodiciy. I.B. Simple measures of persisence I.B.. Firs order auocorrelaion coefficien (FOAC). A recursive and rolling approach. The recursive mehodology derived from Brown, Durbin and Evans (975) consiss in esimaing a parameer using sub-samples =,...,k, for k = k,...,t, where k is he sar up value and T is he full sample size. Unlike recursive esimaion, rolling parameers are compued using sub-samples ha are a consan fracion δ of he full sample. In his way we can keep consan he marginal weigh of each observaion. Using his mehodology we can obain rolling and recursive esimaions of he FOAC for each series y which is calculaed wih he following expression: r k = T = k + ( y y )( y T = ( y k y y ) 2 k T ) ( T k ) where T is he rolling or recursive sample size, k is he number of lags (in his case equal o ), and y k y k ( T k) T = = k + In his way we can analyze he evoluion of his simple measure boh o build an ordinal classificaion of shocks persisence among he series and o evaluae is sabiliy along ime for he differen cycle calculaion mehodologies. I.B.2. Relaive persisence measure (RPM) This measure of persisence resuls from comparing he sum of he firs six auocorrelaion coefficien of he series wih he ones of a series obained as he average of 2 Mone Carlo Simulaion of random walk series wihou drif. RPM = 6 6 RW rk k= k= 6 RW rk k = r Xi k (8) (9) 3

8 where RW is an arificial random walk series, Xi is he i h series (in log., sochasic cycle and deerminisic cycle), r and r are he k order auocorrelaion coefficien for he RW and Xi RW k Xi k respecively. If RPM indicaor for a seleced series are close o uniy, no significan difference beween his series and an I () variable exiss. When RPM>, he series presens bigger shock s persisence han a uni roo process, so i is possible ha i is an I (2) variable. On he oher hand, a RPM significaively lower han one is usually found in saionary variables. I.C. Tes of Uni Roos Nelson and Plosser (982) demonsraed ha a ime series has a sochasic rend if and only if i has a Uni Rood (UR) in he auoregressive componen. In such a way, esing for he number of UR is equivalen o esing he exisence of a sochasic rend. Based on he fac ha he parameer d in an ARIMA (p,d,q) 6 represenaion is equal o he number of Uni Roos, Dickey and Fuller consruced a es on he null hypohesis of UR. This is he so-called Dickey-Fuller (DF) es. Since i is based on he resricive assumpion of independen and idenically disribued (i.i.d.) errors, several modificaions of he es where developed allowing for some heerogeneiy and serial correlaion in errors. The mos known and used are he Augmened Dickey-Fuller (ADF) es and he semi-parameric alernaive of he (Modified) Phillips-Perron es (Phillips and Perron, 988, for he original es and Perron and Ng, 996, for he modified version of he es). Nelson and Plosser used hese ess, in he line of he original DF es. Sargan and Bhargava (983) posulae a differen approach presening heir es in a Durbin-Wason framework. Basically, he idea of he DF es is o check he null hypohesis of ρ = in he following equaion: y = α + ρy - + ε () The mechanism consiss on esing he null of ξ= in he Ordinary Leas Squares (OLS) regression in he following equaion, which is equivalen o (): y = α + ξy - + ε () where ξ = ρ -. Rejecion of he hypohesis ξ = in favor of he alernaive ξ < implies ha ρ < and ha y is inegraed of order zero (). If we canno rejec ξ =, hen we should repea he es using y in place of y. The Dickey- Fuller equaion changes o: y = ξ y - + ε (2) The ess based on he DF have differen disribuions for he null and alernaive hypohesis. If y is I (), as indicaed by he null hypohesis, hen equaion () represens a regression of an I () variable on an I () one. In his case here is no limiing normal disribuion. The disribuion used is known as he Dickey-Fuller disribuion. Fuller (976) abulaed he original criical values. MacKinnon (99) and Cheung and Lai (995) modified he criical values o ake ino accoun he effec of differen sample sizes and number of lags. For an acue criic on some of he problems of he ess based on he DF mehodology see Maddala and Kim (998). One weakness of he DF es is ha i doesn ake ino accoun he possible auocorrelaion beween errors ε. If his was he case, he OLS esimaions in equaion () or is subsiues would no be efficien. The soluion, implemened by Dickey and Fuller (98), was o include as explanaory variable de lagged dependen variable. This soluion is known as he Augmened Dickey-Fuller es (ADF). Then, an equivalen equaion o equaion () is: 6 p indicaes he order of inegraion of he auoregressive componen, q is he moving average componen and d he number of imes he variable has been differeniaed o reach saionariy. 4

9 y k = ξ y + Σ ξ y + ε i i= The esing procedure is he same one as before and i is based on he corresponding o he ξ. The criical values are he same ones as hose for he DF es. Phillips (987) and Phillips and Perron (988) proposed a new es using a non-parameric correcion for he presence of serial correlaion. The objecive was o eliminae he nuisance parameers on he asympoic disribuion caused by he presence of serial correlaion in he errors ε. This saisics are known as Z ρ and Z. For he case of an AR () wihou drif 7 : 2 2 ( s se ) Z ρ = T ( ˆ ρ ) (4) 2 T 2 2 T y Z Se = s ˆ ρ 2 s( T Σ ( s 2 2 T Σ s y ) ) 2 e 2 / 2 Cochrane (99) remarked he low power of he Uni Roo ess as well as of any oher es where a null hypohesis of ρ=ρ agains he alernaive ρ -κ wih κ small for reduced samples. Alhough he difference beween ρ y ρ -κ could be reduced and even insignifican from he economic poin of view, his is especially problemaic in he case of Uni Roo ess for here exiss a disconinuiy in he heory of disribuion in viciniy of he uni roo. Thus, in such cases, hese ess would no answer he quesion of which is he mos appropriae disribuion for small samples. I.D. Rolling and Recursive ADF es for Uni Roo Anoher alernaive o es uni roo consiss in evaluaing he shifing roo hypohesis. For his purpose he recursive and rolling developed by Banerjee, Lumsdaine and Sock (992) provides a complee se of analysis. Applied o he Uni Roo Hypohesis, he procedure consiss in esimaing rolling and recursively 8 he maximum and minimum ADF saisics and comparing hem wih he 5% asympoic criical values. In addiion, we analyze he difference beween he maximum and minimum ADF saisics, which can be associaed wih a measure of shifing roo or roo volailiy. I.E. Variance raio measuremen (VR) An alernaive non-parameric insrumen o evaluae he presence of a uni roo is o measure he degree of persisence. Cochrane (988) proposed such alernaive. Using Beveridge and Nelson s (98) decomposiion we can see ha each series can be modeled as a combinaion of a non-saionary random walk (RW) and a saionary componen. However, he RW can have an arbirarily low variance, so ha he power of he UR ess is arbirarily low for small samples. Cochrane (99) highlighs he imporance of measuring he size of he RW componen hrough he degree of persisence of he shocks in he levels of he series. The measuremen presened by Cochrane (988) is as follows: VR k V = V k var( y y = k.var( y y ) ) k If y is saionary, hen lim k! VR k = and if y is a RW, VR k = for any lag size. A direc esimaion for VR is he following: (3) (5) (6) 7 For he cases of an AR () wih a drif, and wih a drif and a linear rend see Maddala and Kim (998). 8 As was explained in he secion.2. for he recursive and rolling esimaion of he FOAC. 5

10 VR k = σ 2 k σ In pracice, several values for VR k are considered and he null is rejeced if a leas one of he VR k generaes evidence agains i (Maddala and Kim, 998). I.F. Uni Roo under he hypohesis of a Srucural Break The idea of a srucural break is associaed wih changes in he parameers in a regression. Discussions on he consancy of parameers have been very rich in economerics, wih a grea number of es developed wih respec o he maer (for a review and classificaion see Maddala and Kim, 998). The poin ha we are ineresed in focusing on for his sudy is how srucural changes can affec he resuls for he Uni Roo ess. A pioneering aricle on he subjec was one by Perron (989) where he argues ha, in general, shocks are ransiory and he series are sporadically hi by exraordinary (no regular) evens. Since is probabiliy disribuion is differen o ha of oher regular shocks, he proposes changing hem from he noise componen o he deerminisic rend of he series. In oher words, innovaions are ransiory (and so saionary) around a deerminisic rend ha can sporadically suffer changes of differen kind (in he consan, in he slope, or boh). Perron s proposal is very srong and pus back ino discussion wha had consolidaed as he dominan framework in he 8s on he exisence of a sochasic rend in he majoriy of he economic ime series. Tha is, ha hey were generaed by a DSP. For example, he exisence of a srucural break represened by a change in he value of he mean in a series could make he convenional analysis conclude ha here exiss a uni roo when in realiy none exiss. I is jus ha he series was and is sill saionary, bu now around a new mean. Charenza and Deadman (997) indicaes ha he mos simple case of a saionary series I () ha suffers a jump (srucural break) in he mean in he middle of he sample could be described by a random walk wih drif of he kind: y = α + ρy - + ε (8) wih ρ = 9. The conclusion is ha he auoregressive equaion could bias ρ owards. In his case, in he presence of a srucural break, he ess of he Dickey-Fuller kind end o accep he null hypohesis of a Uni Roo when acually he process is saionary o boh sides of he srucural break. Perron applies he es o Nelson and Plosser s series and find ha he hypohesis of Uni Roo mus be rejeced in all of he series wih he excepion of he Consumer Price Index, he velociy of money and he nominal ineres rae. For ha reason, he considers ha he majoriy of he series have a segmened linear rend. From Perron s work on, here has been a long sequence of ess ha gained in complexiy. In Perron (989) he proposes a modified DF es for Uni Roo in he noise funcion wih hree differen alernaives for he deerminisic rend funcion of he series (DT ). In he firs one he allows for a srucural change refleced in he inercep (crash model). Model A: DT = α + βdu + δ (9) where a) DU = if > T b ; oherwise. The second model only allows for a change in he slope (changing growh model). Model B: DT = α + δ + δ DT* (2) where b) DT* = -T b if > T b ; oherwise. The hird model gives place o changes boh in he inercep and he slope. Model C: DT = α + βdu + δ + δ DT* (2) (7) 9 Remember ha a random walk wih drif is equivalen o a deerminisic rend. 6

11 The sraegy followed by Perron is o firs de-rend he series and hen analyze he behavior of he residuals. Perron hen obains he limi disribuion wih he Ordinary Leas Squares of he normalized esimaors of ρˆ and he corresponding -saisics of he following regression: y i = ρ i y - + ε (22) i where: y wih i = A, B, C being he residuals of he regression of y corresponding o each of he models. The es by Perron is a condiional es for a given srucural break poin, which is defined exane. For his reason, i is criicized for he possibiliy of pre-esing bias. Since his proposal, here have been several aemps o give endogeneiy o he srucural breaks by using recursive, rolling and sequenial ess. The firs wo ake sub-samples, from he general sample, ha may grow or remain fixed (wih a consan marginal weigh for he new daa poins); meanwhile, he sequenial es progressively increase he dae of he hypoheical break by using differen dummy variables. The endogeneizaion of he srucural break generaed several papers ha revered previous Perron resuls, bu when he exisence of more han one endogenous srucural break is allowed, he number of rejecions of he UR hypohesis once again increases. Perron (993, 994a, 994b) and Volgelsang and Perron (994) propose wo models o allow for endogenous srucural changes: Addiive ouliers (AO) model and Innovaional ouliers (IO) model. The difference beween he wo models is in he way hey undersand he change. In he AO model he change is abrup while in he IO change is gradual and is affeced by he behavior of he noise funcion since i moves in a similar way as he shocks ha affec his funcion (Cai, 997). For AO models he hree kinds of srucural changes seen before (A, B and C) are applicable while for he IO modes only A and C are. The B version in he IO models is no ofen used in empirical applicaion because i is no easy o apply when using linear esimaion mehods. The AO model is performed using a wo sep regression procedure, for he case of change in he slope of he rend funcion when he segmens are joined a he ime break. The poin is o es he -saisics of ρ =. Le DT = T b if >T b ; and oherwise wih T b he ime of break. The firs sep consiss on esimaing he following regression: y = µ + β + γ DT + ~ y Laer, he error erm ( ~ y k = ~ y + Σ c j ~ y j j= ρ + ε y~ ) is modeled as follows: We can obain he IO models analyzing hem separaely under he null and he alernaive hypoheses. In he firs case (under he null), using Perron s (994) noaion, we can describe model A as follows: IO, Model A : y = y + b +ψ ( L)( e + δd( Tb ) ) (25) Similarly, he expression for Model C is: IO2, Model C : y = y + b + ψ ( L)( e + δd( T ) + ηdu ) (26) b where b is he drif componen, ψ (L) is he lag polynomial or moving average represenaion of he firs difference of y, D ( T b ) is a pulse dummy variable (he change in he inercep of he rend funcion of y, observed from he firs difference of y ) equal o if = T b + and oherwise, and DU is anoher dummy variable, bu in his case i is equal o if >T b and oherwise (represening he change in he slope of he rend funcion observed from he firs difference of y ). (23) (24) 7

12 According o hese represenaions he immediae impac of he change in he inercep is δ, while he long run impac is ψ ( ). δ. In he same way he immediae and he long run impac of he change in he slope areη and ψ ( ). η, respecively. In he second case (under he alernaive hypohesis) Models A and C are: IO, Model A 2 : y = µ + β + Φ L)( e + θdu ) (27) ( * IO2, Model C 2 : y = µ + β + Φ( L)( e + θdu + γdt ) (28) where µ is he inercep of he rend funcion, β is he slope of he rend funcion, Φ (L) is he lag polynomial or moving average represenaion of y, DU is a dummy variable equal o if >T b and oherwise. In hese models DU represens he change in he inercep of * he rend funcion since i is observed from he level of y, and DT is anoher dummy variable equal o - T b if >T b and oherwise. This variable represens he change in he slope of he rend funcion. For hese equaions, he immediae impac of he change in he inercep is θ, and he long run impac is Φ (). θ. For he change in he slope, he immediae and he long run impac of are γ and Φ (). γ, respecively. To es for he presence of a uni roo we can nes he null and he alernaive hypohesis in boh models (A and C) in he following way: IO, Model A 3 : IO2, Model C 3 : y y k + ci y i + i= = µ + θdu + β + δd( T ) + ρy e (29) b k + ci y i + i= * = µ + θdu + β + γdt + δd( T ) + ρy e (3) where he coefficien c i is he auoregressive represenaion of he moving average polynomial ψ ( L). The saisic of ineres is he -saisic for esing ha ρ =. Togeher wih he oher coefficiens, ρ deermines he specific form of he Daa Generaion Process. I.G. A synhesis of he differen views Table a presens a synhesis of he exising views wih respec o he rend ha is characerisic of a series, is relaionship wih he shocks and is effec on he cycles. [Table abou here] b A sochasic rend implies ha each shock is permanen and for ha reason is usually called a real shock. In his case, he series presen high persisence coefficiens. A deerminisic rend, on he oher hand, implies ha shocks ha hi he economy do no deviae i permanenly from is long run pah. Thus, every shock is ransiory. Assuming a segmened rend implies ha he majoriy of he shocks are ransiory and ha only one (or a few) is permanen. These are he srucural breaks ha hi he economy very sporadically. For he case of Argenina, his could be associaed wih evens such as he deb crisis, he converibiliy, he Mercosur, he reurn of democracy or he hyperinflaion. The resiuion of he deerminisic rend, even hough segmened, o he cener of he scene has grea implicaions wih respec o he role of shocks and of sabilizaion policies. Accordingly, i s been he source of grea conroversies, giving place o a se of comparaive sudies on previous works on Uni Roo and allowing he possibiliy of gaining greaer precision in he specificaion and knowledge of he macroeconomic ime series. 8

13 Clearly, hese improvemens in he analysis of he daa generaing process (DGP) should allow for greaer precision in he search for he cycle and is feaures. I.H. The mehodology The objecive of his paper is o combine a baery of complemenary ools o deermine he bes approximaion o he cycle of some of he mos relevan macroeconomic ime series for Argenina. Here we presen a procedure (ha we will follow in he res of paper) o check for he exisence of saionariy or no in he series (and he influence of his fac in he cycle of he variables), as well as for comparing he differences beween he cycle assuming a linear rend and a purely sochasic rend (firs differences). Our mehodology consiss on he following seps:. Analyze he firs order auocorrelaion coefficien of he series (of he cycle of hose series) including a recursive and rolling version. The goal is o obain a firs vision of he level of persisence of he series and of he possible changes in he inra-sample behavior. 2. Compare he persisence of he series wih respec o ha of an arificial series consruced as he average of 2 Mone Carlo simulaions of RW processes. This will allow us o build a Relaive Persisence Measure (RPM). 3. Analyze for he hypohesis of Uni Roo for he sample as a whole wih he Augmened Dickey-Fuller (ADF). 4. Perform he analysis of he hypohesis of Uni Roo for he whole sample wih he Phillips- Perron (PP) es. 5. Analyze of he hypohesis of Uni Roo for he sub-samples wih a recursive ADF, obaining he maximum and minimum. 6. Evaluae he hypohesis of Uni Roo for he sub-samples wih a rolling ADF, obaining he maximum and minimum. 7. Perform of he Variance Raio (VR) for a sequence of k ha is sufficienly long. 8. Analyze of he hypohesis of Uni Rood in he presence of srucural break: Perron s es wih exogenous selecion of he break dae. 9. Check he hypohesis of Uni Roo in he presence of srucural break: Perron s es wih endogenous selecion of he break dae: addiive ouliers (AO).. Analyze he hypohesis of Uni Roo in he presence of srucural break: Perron s es wih endogenous selecion of he break dae: innovaion ouliers (IO).. Evaluae of he informaion from he ess on he characerisics of he DGP and hus he bes specificaion for he permanen componen of he series. Following his sequence of growing complexiy we begin wih he eye inspecion of he correlograms, hen move o he radiional Uni Roo ess, double checking wih he indicaors of persisence and analyzing if here are changes in he order of inegraion of he series under he hypohesis of srucural break and evenually deermine when hey occurred. We believe ha his is an imporan conribuion since as far as we know such an inegral analysis does no exis. We ve found as an immediae aneceden, hough parially relaed o our work, he imporan paper by Sosa-Escudero (997). However, he ineres here falls exclusively on he GDP. Addiionally he series only reaches he year 992. Anoher work, also parially relaed o ours, is ha of Ahumada (992) on coinegraion in nominal variables. Surzenegger (989) analyzes he kind of shocks affecing Argenina s GDP using Blanchard and Quah (989) decomposiion. For more recen sources ha include mos of he converibiliy period (which begun in 9:2) Carrera, Féliz and Panigo (998a, b) presen he resuls for he GDP and inflaion in he firs paper and on he real exchange rae in he second one. However, no one has followed an inegral approach such as he one presened in his paper. 9

14 I.I. The daa For his paper we use he daa provided by he Argeninean Governmen s Saisical Office (INDEC), he Minisry of he Economy and Public Works, he Cenral Bank and he Economic Commission for Lain America and he Caribbean (ECLAC). The daa was provided by is source in quarerly periodiciy (for he period 98: - 998:4) in every case wih he excepion of he unemploymen rae, he paricipaion rae and employmen rae which are of semi-annual periodiciy (for he period 974: - 998:2). The GDP, Invesmen and rade balance were provided by he Minisry of he Economy and Publics Works, while wages, CPI, Paricipaion rae, Unemploymen rae and Employmen rae where provided by he INDEC. We used he passive nominal annual ineres rae as he proxy for he ineres rae wih informaion provided by ECLAC. Finally, daa on M and he nominal exchange rae (used o calculae he real exchange rae) were provided by he Cenral Bank of Argenina (BCRA). The rade balance is presened as a percenage of GDP. The daa was ransformed by seasonally adjusing i using he X- ARIMA mehodology, excep for he semi-annual variables. We hen applied he logarihm funcion o he series, wih he excepions of he nominal ineres rae, he rade balance, M growh, inflaion and he semi-annual variables which were lef unouched because hey are all expressed in percenages. We use he sofware package RATS 4.2. The real exchange rae was calculaed from he nominal exchange rae of he Peso o he American dollar, correcing i by he evoluion of Argenina s and American s consumer price index (CPI). We analyze separaely M and M growh, he CPI and inflaion (CPI growh) because he log approximaion of growh for hese series is no applicable due hey presen srong oscillaion in his sample period. The idenificaion codes of each series are presened in Table 2 in he Appendix a he end of he paper. II. MEASURES OF THE PERSISTENCE OF THE MACROECONOMIC SERIES IN ARGENTINA II.A. The cycle The mos radiional (and mos ofen used) way of exracing he cycle relies in a linear deerminisic rend such as he one presened in Figure. The resul is wha s called a deerminisic cycle indicaed by he hick race in Figure 2. There we can idenify 5 cycles ha allow us o inerpre he mos relevan momens for he macro-economy in Argenina since he 8s. [Figure and 2 abou here] The firs one, ending in 982, shows he end of he miliary governmen. I is dominaed mainly by he surge and decadence of he monearis sabilizaion plan (which begun in 978) based on a pre-announced rae of devaluaion ha resuled o he unsusainable appreciaion of he currency (he Peso) and laer in a huge financial crisis. The cycle is he resul of he shuing down of he inernaional financial markes afer he Mexican defaul, he change in he poliical mood wih he reinsiuion of democraic rule, he saizaion of he privae exernal deb and several inens of wages and salaries recomposiion in he ransiion o democracy. The hird cycle accompanies he sabilizaion plan know as Plan Ausral which include a moneary reform, a fixed nominal exchange rae, and an incomes policy (amongs oher insrumens). This plan had an iniial successful sage associaed wih he reducion in he inflaion rae. The deep recession in he years following he failure of he plan, are associaed wih he progressive loss of macroeconomic insrumens ha derived in a number of (ever) shorer and more ineffecive programs ha ended up in hyperinflaion in 989. Wih he change of governmen, also in 989, we observe a small cycle ha coincides wih he firs sabilizaion plan ried during Menem s governmen, which was based on exchange rae

15 fixaion wih almos no inernaional reserves. This led he economy o is lowes level in he period in he firs quarer of 99. To grasp he deph of his recession, see, for example, ha he GDP a ha ime was % lower in real erms han i was in 98 (and more han 2% below is long-run deerminisic rend). The fourh cycle sars wih a new program based in a floaing exchange rae. One of he mos drasic credibiliy measures was aken: o change all of he Sae s shor erm deb and people s bank deposis, ha generaed he Cenral Bank s huge defici, ino long run deb (nominaed in dollars). The program couldn avoid a new hyperinflaionary shock bu i help recover much of he Cenral Bank s foreign reserves. This would be key for he move o a new exchange rae fixaion where full converibiliy of local currency is assumed and he Cenral Bank s reserves covered he full moneary base (currency board regime). Known as he Converibiliy Plan, his has been he mos successful experience as regards a sabilizaion plan. Togeher wih he effeciveness of he insrumens used, he program ook advanage of he newly re-opened inernaional financial markes and he imporan reducion in he inernaional ineres rae. In fac, his phase of he cycle wih srong growh was inerruped by he recessive crisis resuling from Mexico s devaluaion in 994 (known as he Tequila effec). The las cycle idenifies wih he expansion ha begun in 996, resuling from he reducion in he inernaional ineres rae and he fac ha he converibiliy resised he previous negaive exernal shock. The new urning poin is associaed wih he inernaional crisis following he crisis in Souh Eas Asia. II.B. Wha cycle? When we use a deerminisic linear rend such as ha in Figure, he cycle we obain is much wider han he one we could ge from a sochasic rend. There exis muliple possible sochasic rends. Following he crierion of using he simples model, we calculaed he sochasic cycle as firs differences of he logarihm of he series (which for small changes approximae he raes of growh of GDP). In Figure 2 we see he differen behavior of he wo cycles. In wha follows we ll call Cycle o he one coming from he sochasic rend and Cycle 2 o he oher one, resuling from he deerminisic rend. From he comparison, i is eviden he differen variance in boh cycles. Cycle is more homogeneous han Cycle 2 (which shows a behavior wih he shape of a V resuling from he deep recession of and he wo expansions of he nineies. Defining which kind of cycle is he relevan one has imporan implicaions as regards associaing economic policies o objecives. Inuiively, we could hink ha such a poin is showing a very srong srucural break, especially when from he analysis of he facs i appears as a poin of economic change due o he hyperinflaionary shock and he change of governmen. We ll leave for he end of his paper he formal es for his possibiliy in an ad-hoc manner as well as endogenously o he daa generaing process. The problem ha appears wih he GDP is common wih he res of he variables so we ll follow our sequenial mehodology o ry o esablish wha is he mos appropriae DGP for each one. II.C. Simple measures of persisence II.C.. Firs order correlaion coefficiens (FOAC) Following he mehodology described in secion, we obain he firs order auocorrelaion coefficiens (FOAC), recursive and rolling, for each variable which are presened in figure 3 in he appendix. We find as a common fac ha he recursive coefficien in almos all variables grows owards he end of he sample. Amongs he nominal variables such as nominal ineres rae (TN), M growh (DM) and inflaion here s an abrup fall in he levels of auocorrelaion when we include o he sub-sample he daa for he year 988. In he labor marke series i sands ou he increasing auocorrelaion of he unemploymen series. The rolling coefficiens show differen resuls only a he end of he sample, ha is, when we inroduce he years For he real exchange rae, however, we deeced grea sabiliy in he coefficien. Meanwhile, he employmen in he period shows a ransiory, bu abrup, drop in he coefficien.

16 For he cycles, he resuls indicae a highly uniform behavior beween he series. Cycle (Sochasic rend) has low auocorrelaion, rapidly revering o is mean, while cycle 2 (Deerminisic rend) presens auocorrelaion coefficiens of around.9 for he majoriy of he series. For he case of he GDP, and complemening wha has already been seen in Figure 2, he FOAC of cycle is zero while for cycle 2 is.9. In he nominal variables is imporan o highligh he srucural change ha is apparen wih he inclusion of he year 988 (he las sabilizaion plan of he Radical governmen) The nominal ineres rae, M growh and inflaion show coefficiens ha fall o half is value, in cycle 2, or even become negaive, in cycle (Sochasic rend). II.C.2. Relaive persisence measure (RPM) From Table 3 we find paerns of behavior ha can be divided ino 3 differen groups and which are highly sable when we evaluae he series in levels as well as when we evaluae he cycles. Nominal wages, M and he Consumer Price Index (CPI) all show he highes coefficiens, hem being poenially I () and even maybe I (2) series. In he oher exreme, here s he group of he leas persisen series: he nominal ineres rae, he growh in M, inflaion and employmen. This group even shows negaive coefficiens for he sochasic rend process. For he sochasic cycle we should also include in he lowes persisence group he real wages, unemploymen and he paricipaion rae. Finally, in he inermediae group we have he GDP, invesmen, he rade balance and he real exchange rae and, excep for he sochasic cycle, he real wages, unemploymen and he paricipaion rae. As we can see from his indicaor here is a remarkable sabiliy in he composiion of he groups across he differen specificaions (levels, cycle and cycle 2). However, we should highligh he fac ha he value of his indicaor (like he FOAC) is srongly affeced by he derending mehodology. For example, he GDP shows values of.9,.2 and.73 for levels, cycle and cycle 2, respecively. The differen de-rending mehodologies show srongly conradicory resuls and for his reason i is necessary o search deeper ino he srucure of he daa generaing process (DGP) for each series. In he following secion we ll check for he exisence of Uni Roo in he auoregressive componen of he series using he convenional ess. II.D. Uni roo ess II.D.. Augmened Dickey-Fuller (ADF) and Phillips-Perron (PP) These are he mos ofen used ess in inernaional papers on Uni Roo, and hus mos useful for inernaional comparisons, even hough several criicisms could be expressed abou hem as we ve seen in secion. For choosing he number of lags in he ADF es we followed he General o Specific mehodology. Beginning wih 6 lags we esablished for each series he adequae number of lags for he logarihms of he levels as well as for he firs differences of he series. The greaes number of lags was used for he GDP and he real wages and he lowes for he real exchange rae. For he Phillips-Perron es (PP) we esablished a uniform number of lags following he Newey-Wes (994) crierion ha suggess hree lags for quarerly series. Wih respec he srucure of he es as regards wha kind of deerminisic regressors o use we checked in each case he significaiviy of using a consan (C), a consan and a rend (C, T) or none of hem (NDR). In almos all cases for he firs differences we used no deerminisic regressors. The criical values used are hose from MacKinnon (99). The resuls of he ess are shown in Tables 4 and 5. Wih respec o he resuls of he ess, we found ha almos all he series are I () under boh ess wih a conservaive hypohesis of 5% significaiviy. Concenraing in he discrepancies of he ess, we found ha hese are mos common in nominal variables (as we found in he measures of persisence in he previous secion). Firsly, we see he series ha presen mixed evidence as regards being I (). 2

17 One of hem is he nominal ineres rae for he PP es which resuls I () for any alernaive criical value while i appears o be I () for he ADF es, also under any criical value. I is ineresing o noe ha his difference appears even hough he deerminisic regressors are he idenical in boh cases. The growh in M (dm) resuls consisenly saionary I () in boh ess for almos every criical values. Only for he ADF es a % he series appears o be I (). Inflaion is anoher series considered I () for boh ess a 5%. M (he log level) is an I (2) series for boh ess, somehing which is consisen wih he fac ha a % dm was I (). Only a % does M appear o be I () in he PP es. The consumer price level (CPI) is anoher series ha shows srong discrepancies beween he ess. For he ADF es i is I (2) while for he PP es i is an I () series. In he case of he ADF he resul is consisen wih he fac ha inflaion is I () a %, while he resul for he CPI wih he PP es is consisen wih inflaion being I () in ha es. I is probable ha he ess are capuring he problems of he hyperinflaionary shocks o he economy in differen ways. Wih respec o I () series i is sriking he number of hem ha fall in his caegory: no only he GDP and invesmen, bu also variables such as he real exchange rae and he rade balance. The indicaors from he labor marke are also I () wihou excepion, from wages (nominal and real) o variables such us he unemploymen, employmen and he paricipaion rae. Wih such srong resuls we should begin quesioning wheher his characerisic is caused by he exisence of a Uni Roo or is jus he resul of a srucural shock ha biased he ρ coefficien owards. This problem will be looked a more deeply in he following seps of he paper. II.D.2. Recursive and Rolling Augmened Dickey-Fuller Recursive and rolling esimaion of ADF saisics was developed aking k = δ = 28 observaions for quarerly daa and k = δ = 2 observaions for semiannual daa. The sochasic and deerminisic regressors for he rolling and recursive equaion are aken from ADF es for he enire sample. The esimaed saisics are presened in he Tables 6 o 7 and in he Figure 4 of he appendix. The abulaed 5% criical values are aken form Banerjee e al (992). In he Figure 4 we presen boh he Banerjee e al (992) and he Cheung and Lai (995) 5% criical values for he minimum ADF saisic. We can summarize hese resuls as follows: The null hypohesis of uni roo can no be rejeced for any of he variables when recursive mehodology and Banerjee s 5% criical values are used. If we ake he Cheung and Lai s 5% criical values for he minimum recursive ADF saisic, M growh and inflaion become I () in he nineies (he only roos ha shif wih his mehodology). In he rolling esimaion he main resul is he srong roo volailiy. For more han 5% of he variables he difference beween he maximum and minimum rolling ADF saisic is bigger han he abulaed criical value. This can be aken as a parial evidence of he exisence of srucural breaks. Excep for real wages, all prices and moneary variables presen a saionary period a he end of he sample (of variable duraion ). However his resul migh be a consequence of he disappearance of he effecs of hyperinflaion since a he end of he sample, he rolling mehodology does no ake ino accoun he observaions of ha period. The quesion is if he I () behavior is he consequence of ouliers from he hyperinflaion period or he resul of he change of regime wih he converibiliy. Finally, here exiss srong sabiliy in he resuls for he Naional Accouns (GDP, invesmen and rade balance) and labor marke variables (wih he excepion of nominal wages and unemploymen rae). All of hem have been I () for each sub-sample wih he recursive as well as wih he rolling esimaion mehodology. Neverheless, for M, real exchange rae and nominal wages his period is exremely shor (3, 5 and 5 quarers, respecively), Thus, we can conclude he for hese series he order of inegraion is. 3

18 II.E. Variance raio es (VR) While he ADF is a parameric measure of he persisence of he shocks in a series, he one presened by Cochrane (988) is a non-parameric measure in as much as i does no depend on he selecion of he model. In his sense i is a complemenary measure o he convenional Uni Roo ess. In Table 8 we presen he Variance Raio Tes (VR) for each series in he period following he mehodology describe in secion. If we ake as a reference he VR value afer 2 quarers we are able o classify he series in four groups. The firs one includes hose variables whose variance grows explosively and have values ha end o 4. Here we find he nominal wages, he CPI and M. No only do hey show a big number bu hey also show a rend in ha value o grow. This seems o indicae ha he series could be I (2) as i was he case for hese variables in he previous secion (he ADF showed ha, a % significance, he nominal wages were I (2) oo). Amongs he variables ha afer 2 quarers sill have a persisence of close o we find he GDP (.), he real exchange rae (.87), he rade balance (.6) and invesmen (.6). These series are hose bes associaed wih he idea of I () series. The nominal ineres rae, growh in M and inflaion show values of VR! when k!. This is a srong indicaion of a saionary series. The variables of he labor marke (wih he excepion of he nominal wages) conform an independen group wih inermediae persisence beween.25 and.64. This could be an indicaion of he exisence of fracional inegraion (Sowel, 99) or a srucural break. II.F. Uni roo ess under srucural break The possibiliy ha a srucural break is he cause why many series ha are rend saionary (TSP) appear o be I () has been he greaes challenge pu forward by Perron o he resuls accumulaed since Nelson and Plosser s original paper in 98. In a grea number of papers from his auhor, his mehodology has been consolidaing in response o he much of he iniial criicism. Perron s firs es is a condiional es where he dae of he srucural break is esablished exogenously by he analys. One of he mos imporan criicisms resuled from he fac ha his produced a pre-esing bias in favor of he non-rejecion of he null hypohesis of srucural break. The condiion of independence in he disribuion wih respec o he daa was no saisfied. For ha reason, Perron (994) and Volgelsang and Perron (994) developed a esing mehodology ha allowed for he endogenous deecion of he break dae. Wih respec o he use of a priori informaion, Maddala and Kim (998) sae ha his criicisms is parially unjusified since i would no make sense o look for a srucural break in he whole sample when we know ha here is a significan even. According o he auhors, he search should be performed around his even. In his paper, we do exacly ha wih he change of governmen in 989:II and he converibiliy in 99:I. Following he seps in our mehodology from secion, we ll analyze he minimum saisic for ρ= in order o deec he srucural break in he endogenous alernaive, selecing i a priori in he exogenous one. II.F.. Perron uni roo es wih exogenous srucural break In Table 9 we presen he resuls for Perron s Uni Roo es wih exogenous srucural break for every variable analyzed in his paper. In each one we esed he hree alernaive models presened in secion : A) Crash model, ha allows for a change in he consan, B) Changing Growh model, ha allows for a change in he rae of grow or slope, and model C) ha allows for a simulaneous change in boh consan and slope. The criical values for he ess can be found in Perron (989). As regards he daes of he breaks, afer a qualiaive analysis of he series we decided o use as break dae for he GDP and he oher real variables he hird quarer of 989 (89:III) since i coincides wih he lowes poin for mos of hem and wih he coming o power of a new governmen ha implemened a srong se of policies of srucural changes o gain credibiliy. 4

19 For he nominal variables, on he oher hand, he mos relevan srucural change seems o have been daed in he second quarer of 99 (9:II), wih he beginning of he Converibiliy Plan (currency board) ha, as we ve already seen, dramaically reduced o inernaional sandards he raes of change and he volailiy of hese variables. Wih respec o he real wages we chose as a srucural break he hird quarer of 984 (he las Keynesian aemp o increase real wages) since from ha dae on he variable changed is growing rend and begun o fall. In general erms, he es changed only parially he resuls of he convenional ess of Uni Roo (ADF and PP) or hose of he persisence measures (VR). The GDP, he nominal wages, he rade balance, invesmen, unemploymen and employmen are I () series even hough we allow for he exogenously se srucural change. In he case of he nominal ineres rae, in any of he specificaions (A, B or C) i appears o be I (), in conras wih he resuls for he ADF es and confirming he resul of he PP es and he VR ha showed a value of.9. In he case of M, he series appears o be I () for every model, conradicing he ADF and PP ess, as well as he VR which showed a value of Consisenly, dm is I (), confirming he resuls of he hree convenional ess. In he case of he CPI, he variable is I () for every model and his conradics he ADF and VR resuls bu confirms he PP es. In he case of he real wages and he real exchange rae if we allow for a break in he slope and in he consan respecively, boh show he series o be I () a 5%, conradicing he previous resuls from he ADF and PP ess. However, anicipaing his resul he VR showed an inermediae value for boh series (.64 and.87). Lasly, he rae of paricipaion urns I () when we allow for a change in he slope or in he slope and he consan simulaneously. II.F.2. Perron uni roo es wih endogenous srucural break Of he five possible models, as we ve seen in secion, in Table we presen he hree mos relevan, ha cover he wides number of resuls. The model IO allows for a gradual change in he inercep only, he model IO2 allows for he gradual change in he inercep and he slope ogeher and he AO2 allows for a change in he slope. Wih respec o an imporan byproduc such as he dae of he srucural break, endogenously seleced by each model, we observe grea dispersion. Model IO2 is he one ha mos concenraes he breaks around On he conrary, model IO presens he mos dispersion in he break daes. The real wages and he paricipaion rae presen he oldes srucural breaks, a he beginning of he eighies (approximaely 2 quarers before any oher variable). Comparing beween models, IO model presens 4 variables which are I () a 5%, he IO2 model 8 variable I () while in he AO2 model only 2 variables appear o be I (). Only dm is considered saionary by all hree models. Meanwhile, he nominal ineres rae, inflaion, unemploymen and paricipaion rae are found saionary by a leas wo models. Undoubedly, here exiss a direc relaionship beween he number of series ha change o being saionary and he flexibiliy o admi srucural changes since IO2 is he model ha admis he mos shifing coefficiens. As a firs resul, we highligh he confirmaion of he exisence of a Uni Roo even under he hypohesis of an endogenous srucural break (in any of is alernaives) in 5 of he 4 series: he GDP, he real wages, he rade balance, invesmen and employmen. Amongs he paricular cases, nominal wages, M and CPI appear o be saionary according o model IO2. This conradics every oher es we ve performed for he complee sample (ADF, PP and VR) bu i is consisen wih he resuls of he Rolling ADF for he ending period of he sample, ha is, when he daa from he converibiliy period eners wih is full weigh. In his variables here is a srong discrepancy beween ess abou he dae of he srucural break. IO ess indicae i inside he period while he AO es pus i beween he years

20 Wih respec o he nominal ineres rae, in boh IO and IO2 models i appears o be a saionary series, coherenly wih he PP es and VR bu in conradicion wih he ADF for he complee sample. However, his resul is consisen wih he rolling ADF ha showed saionariy of nominal ineres raes in he las period of he sample (he converibiliy). In he labor marke, he paricipaion rae is saionary under wo alernaives, he same happening wih he unemploymen rae. This conradics he ADF and PP resuls. Wih respec o he measure of persisence, we observe ha boh series had inermediae values, especially he paricipaion rae (.64). These resuls also conradic hose coming from he Rolling ADF where only he unemploymen appears saionary during a brief period of ime. All oher labor marke variable are I (). III. A COMPARATIVE ANALISYS In Table we presen a comparaive analysis for each variable using every es (eleven) proposed in he mehodology. To build a unique indicaor of inegraion, we ook he order of inegraion suggesed by each es for each variable and calculaed he average order of inegraion for every series (Table 2). [Table 2 abou here] Number.5 indicaes ha he series is I () a 5% bu I () a %, a value of saes he series is I () under boh criical values,.5 means he series is I (2) a % bu I () a 5%, while a value of 2 indicaes he value is I (2) a boh 5% and %. In he case of he rolling or recursive ADF ess, a.5 value indicaes ha in an imporan par of he sample he es shows a change from I () for he ADF o I () for he complee sample. The analysis of hese values should be performed ogeher wih he analysis of he dispersion of he resuls amongs he ess (measured by he variaion coefficien) o check for he robusness of he conclusions. A series wih coefficiens equal o and small percenage of dispersion in he resuls can be considered robusly as I (). As he coefficiens ge closer o zero, here is greaer possibiliy ha he ess considered he series as I (). Wih values beween and we require a deailed analysis of he srucure of he resuls of he differen ess. If he rolling ADF and one or several UR ess under he srucural break hypohesis signal an I () series, hen we are in he presence of a variable where he nonsaionariy given by he ess for he complee sample (ADF, PP, VR) is an error induced by an exraordinary even. For ha reason, he series should be considered saionary. Anoher possibiliy is ha he series presens fracional inegraion. Values higher han are an indicaion of I (2) series, alhough we mus be cauious wih regards o he robusness of his resul, since we could find oo much dispersion when working wih sub-samples due o he possibiliy of srucural breaks. From he resul we can see ha he GDP, invesmen and he rade balance are he only hree series ha pass all he ess, so we can consider hem as robusly I (). The assumpion of a sochasic rend when proceeding o exrac he cycle seems o be he bes sraegy o accuraely model he series. In he case of GDP, our resuls are similar o hose of Sosa- Escudero (997) for he period The real exchange rae is a non-saionary variable in he sample as a whole. Only for models AO and IO2 he variable is considered saionary a 5%. However, wih respec o he dae of he srucural break he majoriy of he ess indicae ha i occurred in he hird quarer of 989 (89:III). The nominal ineres rae, dm and inflaion are clearly saionary variables. They presen a srucural break in 989 according o he majoriy of he srucural break ess. This indicaes ha he converibiliy is no he key dae for his series as we had assumed for he case of exogenous breaks. 6

21 M (in levels), he CPI and nominal wages show a srongly non-saionary behavior. For some of he ess in a sub-sample hese series appeared as I (2). Only he IO2 es, which is he mos flexible in allowing for changes, indicaed ha he hree series were I () even a % wih a break dae around 88:IV and 89: where he inercep and he slope changed for he nominal variables in levels. The series of he labor marke have a behavior ha ends o be non-saionary. The value for employmen and real wages is very close o. Employmen is always I () excep for he VR measure where i has a very low persisence,.26. The AO2 es, ha allows he analys o selec he break dae, suggess ha real wages are I () bu only a 5%. I is ineresing o noice ha none of he ess ha allow for he endogenous selecion of he break dae find an I () resul for hese variables. The paricipaion rae and he unemploymen rae have inermediae-high values, which indicae he presence of a srucural break or of fracional inegraion. While he convenional DF ype ess say he series are I (), he VR measure of persisence is very low. The break ess indicae ha unemploymen has a srucural break even hough hey differ srongly as regards he dae of he break (94: for he IO and 89:II for he AO). For he paricipaion rae, he mos ess of srucural break poin o a break ha occurred in he second quarer of 982 (82:II). The break seems o have been a sudden change in he slope. IV. CONCLUSIONS The objecive of his paper is o provide wih a robus mehodology for he analysis of persisence of shocks affecing macroeconomic series and is consequences on he modeling of he cyclical and permanen componens. Our sraegy is o es he saionariy of he series by using a sequence of indicaors in such a way ha we can analyze he problem from 3 converging poins of view: Persisence of he series, Uni Roo (UR) and UR wih a srucural break. We apply his mehodology o he main macroeconomic series for Argenina, wih he following resuls: Depending on he procedure (sochasic or deerminisic rend) used o exrac he cycle of he series, remarkable differences will appear as regards heir persisence. From our mehodology, we can group he series according o is order of inegraion ino four groups: ) The nominal ineres rae, M growh and inflaion are he series ha appear o be saionary. 2) The unemploymen and paricipaion raes appear, wih a greaer degree of persisence in shocks, which indicaes he possibiliy of fracional inegraion. 3) The GDP, real wages, real exchange rae, rade balance, invesmen and he employmen rae is he group of series ha for mos ess appear o be I (), a confirmaion of he Uni Roo hypohesis. 4) Finally, he nominal wages, M and he CPI, which seem o have more han one Uni Roo. For hese las variables, in group 4, he resuls show noorious differences beween he complee sample convenional ess and hose ha allow for srucural change. These variables seem o have changed form I (2) o I () in he nineies. In he case of he mos flexible Uni Roo es wih a srucural change, IO2, 6 ou of he 4 variables resul I () in comparison wih he 9 ou of 4 for he ADF case. Based on he resuls for he series in group 3, he bes srucure for modeling heir cycle seems o come from assuming a sochasic rend in he series. The underlying macroeconomic inuiion is he idea ha shocks affecing hese variables have permanen effecs. Given he fac he GDP is amongs hese, he cycle ha i is mos useful for he analysis of he curren sae Argenina s economy is closer o Cycle in Figure 2, smaller and less variable han he one mos ofen used (Cycle 2 in Figure 2). On he conrary, for series in groups and 2 a deerminisic rend (wih or wihou a srucural break depending on he case) seems o be he mos appropriae sraegy for calculaing he cycle. The kinds of shocks affecing hese series are mainly ransiory. This implies one of wo 7

22 hings: eiher he economy has forces ha auomaically regulae i, revering he deviaions of he series from is rend, or he policy acions aken o avoid he persisence of he deviaions have been effecive. Wih respec o variables in group 4, we recommend a horough analysis, looking for he possibiliy of muliple srucural breaks and/or he correc specificaion of he ime polynomial included in he deerminisic componen of he ess. Finally, wih respec o he dae of he srucural break relevan for he Argeninean economy, he years concenrae he greaes number of breaks deeced endogenously for he series of hese work. Thus, we can conclude ha he converibiliy does no appear o be a poin of srucural change in he daa generaing process of he main macroeconomic series of Argenina. V. REFERENCES. Ahumada, H. (992), "Propiedades emporales y relaciones de coinegración de variables nominales en Argenina", Banco Cenral de la República Argenina, mimeo. 2. Banerjee, A., Lumsdaine, R.L. and Sock, J.H. (992), "Recursive and sequenial ess of he Uni Roo and Trend Break hypohesis: heory and inernaional evidence", Journal of Business and Economic Saisics,, Beveridge, S. and Nelson, C.R. (98), "A new approach o decomposiion of economic ime series ino permanen and ransiory componens wih paricular aenion o measuremen of he Business Cycle ", Journal of Moneary Economics, 7, Blanchard, O.J. and Quah, D. (989), "The dynamic effecs of aggregae demand and supply disurbances", American Economic Review, 79, Brown, R.L., Durbin, J. and Evans, J.M. (975), "Techniques for esing he consancy of regression relaionships over ime", Journal of he Royal Saisical Sociey, Series B 37, Carrera J.E., Féliz, M. and Panigo, D.T. (998a), "Shocks idenificaion in Argenina and Brasil. A Vecor Error Correcion Model", XVI Meeing of he Lain American Economeric Sociey, Universidad Caólica del Perú, Lima, Perú. 7. Carrera J.E., Féliz, M. and Panigo, D.T. (998b), "The meassuremen of he equilibrium real exchange rae. A new economeric approximaion", Anales, XXXIII Reunión Anual de la Asociación Argenina de la Economía Políica (AAEP). 8. Cai, R.C. (998), "Sochasic and segmened rends in Brazilian GDP from 9 o 993", Anales, Sociedad Brasileña de Economería. 9. Cochrane, J.H. (988), "How big is he random walk in GNP?", Journal of Poliical Economy, 96, Cochrane, J.H. (99), "A criique of he applicaion of Uni Roo ess", Journal of Economic Dynamics and Conrol, 5, Cribari Neo, F. (993), "The cyclical componen in Brazilian GDP", Revisa de Economería,, Cribari Neo, F. (996), "On ime series economerics", The Quarerly Review of Economics and Finance, 36, Special Issue, Charenza, W:W. and Deadman, D.F. (997), New direcions in economeric pracice, Edward Elgar Publishing. 4. Cheung, Y. and Lai, K. (995), "Lag order and criical values of he Augmened Dickey- Fuller es", Journal of Business and Economic Saisics, 3, Dickey, D.A. and Fuller, W.A. (98), "Likelihood raio saisics for auoregressive ime series wih a Uni Roo", Economerica, 49, Fuller, W.A. (976), Inroducion o Saisical Time Series, New York, John Wiley. 7. Lo, A.W. and MacKinlay, A.C. (988), "Sock marke prices do no follow random walks: evidence from simple specificaion ess", Review of Financial Sudies,, Lo, A.W. and MacKinlay, A.C. (989), "The size and power of he Variance Raio es in finie samples: a Mone Carlo invesigaion", Journal of Economerics, 4,

23 9. MacKinnon, J.G. (99), "Criical values for coinegraion ess", in R.F. Engle and C.W.J. Granger (eds), Long-run Economic Relaionships, Oxford, Oxford Universiy Press. 2. Maddala, G.S. and Kim, I. (998), Uni Roos, coinegraion and srucural change, Cambridge, Massachuses, Cambridge Universiy Press. 2. Nelson, C.R. and Kang, H. (98), "Spurious periodiciy in inappropriaely derended ime series", Journal of Moneary Economics,, Nelson, C.R. and Plosser, C.I. (982), "Trends and random walks in macroeconomic ime series", Journal of Moneary Economics,, Newey, W.K. and Wes, K.D. (994), "Auomaic lags selecion in covariance-marix esimaion", Review of Economics Sudies, Perron, P. (989), "The Grea Crash, he Oil Price Shock, and he Uni Roo hypohesis", Economerica, 57, Perron, P. (993), "The Hump-shaped behavior of macroeconomic flucuaions", Empirical Economics, 8, Perron, P. (994a), "Trend, Uni Roo and srucural change in macroeconomic ime series", in Coinegraion for he Applied Economis, B.B.Rao (ed), Basingsoke, Macmillan Press. 27. Perron, P. (994b), "Furher evidence on Breaking Trend Funcions in macroeconomic variables", Journal of Economerics. 28. Perron, P. and Ng, S. (996), "Useful modificaions o some Uni Roo ess and dependen errors and heir local asympoic properies", Review of Economic Sudies, 63, Phillips, P.C.B. and Perron, P. (988), "Tesing for a Uni Roo in ime series regression", Biomerika, 75, Plosser, C.I. and Schwer, W.G. (978), "Money, income and sunspos: measuring economic relaionships and he effecs of differencing", Journal of Moneary Economics, 4, Sargan, J.D. and Bhargava, A. (983), "Tesing residuals from Leas Squares regression for being generaed by he Gaussian random walk", Economerica, 5, Sosa-Escudero, W. (997), "Tesing for Uni Roo and Trend Breaks in Argenine real GDP", Económica, XLIII,, La Plaa. 33. Sowel, F. (99), "The fracional Uni Roo disribuion", Economerica, 58, Surzenegger, F. (989), "Explicando las flucuaciones del produco en la Argenina", Económica, XXXV,, La Plaa. 35. Volgelsang, T.J. and Perron, P. (994), "Addiional ess for a Uni Roo allowing for a break in he rend funcion a an unknown ime", CRDE, Universié de Monréal, Cahier de Recherche, No

24 VI. FIGURES AND TABLES Figure Linear Trend Log. of GDP Figure Cycle (Sochasic Trend) Cycle 2 (Deerminisic Trend) 2

25 Table Origin of he shocks Order of Duraion of he shocks Persisence Inegraion of he series Trend Kind of Trend Cycle Type of Counercyclical Policy No real Transiory Low I (O) Deerminisic Linear, exponenial. Greaer ampliude Yes Real Permanen High I(k) wih k Sochasic ARIMA models (RW, ec.). Very small or no exisen No. Srucural reform No real Transiory and a few permanen Low I(O) Segmened deerminisic One or several breaks Greaer ampliude Yes, plus Srucural reform 2

26 Table 2 Order of Inegraion Unique Indicaor of Inegraion % significance 5% significance, I() I(),5 I() I(), I() I(),5 I(2) I() 2, I(2) I(2) 22

27 Table 3. Relaive Persisence Measure Code Variable Log./Raes Cycle Cycle 2 A GDP A2 Wages A3 Real Wages A4 Nominal Ineres Rae A5 M A6 M growh A7 CPI..5.9 A8 Inflaion A9 RER A Trade Balance A Invesmen B Paricipaion Rae B2 Unemploymen Rae B3 Employmen Rae

28 Table 4. Augmened Dickey Fuller Tes for Uni Roo GDP Variable Nominal wages Real Wages Nominal Ineres M M Growh CPI Inflaion Real Echange Rae Trade Balance Invesmen Paricipaion Unemploymen Employmen Tes in: ADF Saisic MacKinnon Criical Values % 5% % Tes Srucure Deerminisic Regresors Log C, T 5 Firs (NDR) 4 Log C 2 Firs (NDR) Log C,T 6 Firs (NDR) 2 Rae C 2 Firs (NDR) Log C 4 Firs C 3 Rae C Firs (NDR) Log (NDR) 2 Firs (NDR) 2 Rae C Firs (NDR) Log C,T Firs (NDR) GDP Percen C,T 3 Firs (NDR) Log C,T 3 Firs (NDR) 2 Rae C,T 3 Firs (NDR) 3 Rae C,T 2 Firs (NDR) Rae C 3 Firs (NDR) Lags 24

29 GDP Variable Nominal wages Real Wages Nominal Ineres M M Growh CPI Inflaion Real Echange Rae Trade Balance Invesmen Table 5. Modified Phillip - Perron Tes for Uni Roo Tes in: P-P Saisic MacKinnon Criical Values % 5% % Deerminisic Regresors Tes Srucure Trucaion Lags Log C,T 3 Firs (NDR) 3 Log C,T 3 Firs C,T 3 Log C,T 3 Firs C,T 3 Rae C 3 Firs (NDR) 3 Log C,T 3 Firs (NDR) 3 Rae C 3 Firs (NDR) 3 Log C,T 3 Firs C 3 Rae C 3 Firs (NDR) 3 Log C,T 3 Firs (NDR) 3 GDP Percen C,T 3 Firs (NDR) 3 Log C,T 3 Firs C,T 3 Rae C,T 3 Paricipaion Rae Firs (NDR) 3 Unemploymen Employmen Rae C,T 3 Firs (NDR) 3 Rae C 3 Firs (NDR) 3 25

30 Table 6. Recursive ADF Tes For Uni Roo. Máx ADF Mín ADF Diff ADF 5% C.V. Máx ADF 5% C.V. Mín ADF 5% C.V. Diff ADF Dae for Máx ADF Dae for Mín ADF GDP I/94 IV/87 Nominal Wages III/89 IV/98 Real Wages II/87 IV/96 Nom. Ineres Rae II/89 III/88 M III/89 IV/98 M Growh III/89 IV/98 Consumer Price Index III/89 IV/98 Inflaion III/89 IV/89 Real Exchange Rae IV/86 IV/98 Trade Balance III/87 IV/98 Invesmen II/87 II/89 Paricipaion Rae I/87 II/98 Unemploymen rae I/95 II/93 Employmen Rae II/83 I/98 26

31 Table 7. Rolling ADF Tes For Uni Roo. Máx ADF Mín ADF Diff ADF 5% C.V. Máx ADF 5% C.V. Mín ADF 5% C.V. Diff ADF Dae for Máx ADF Dae for Mín ADF GDP I/9 I/96 Nominal Wages III/89 IV/96 Real Wages III/95 IV/97 Nom. Ineres Rae II/89 I/98 M III/89 II/96 M Growh III/89 III/96 Consumer Price Index III/89 IV/96 Inflaion III/89 I/97 Real Exchange Rae II/89 IV/96 Trade Balance III/9 IV/88 Invesmen II/9 I/98 Paricipaion Rae I/87 II/92 Unemploymen rae I/95 II/9 Employmen Rae II/83 II/9 27

32 Table 8. Variance Raio. Cochrane s measure of persisence Lags Variable GDP Nominal Wages Real Wages Nominal Ineres Rae M M Growh Consumer Price Index Inflaion Real Exchange Rae Trade Balance Invesmen Paricipaion Rae Unemploymen Rae Employmen Rae

33 Table 9. Perron Uni Roo Tes wih exogenous selecion of TB Model Lags Break dae ρ= CV 5% Inegraion order a 5% GDP Nominal Wages Real Wages Nom. Ineres Rae M M Growh Cons. Price Index Inflaion Real Exchange Rae Trade Balance Invesmen Paricipaion Rae Unemploymen rae Employmen Rae AO 4 III/ I() AO2 4 III/ I() AO3 4 III/ I() AO II/ I() AO2 II/ I() AO3 II/ I() AO III/ I() AO2 III/ I() AO3 III/ I() AO II/ I() AO2 II/ I() AO3 II/ I() AO II/ I() AO2 3 II/ I() AO3 2 II/9..24 I() AO II/ I() AO2 II/ I() AO3 II/ I() AO II/ I() AO2 II/ I() AO3 II/ I() AO II/ I() AO2 II/ I() AO3 II/ I() AO III/ I() AO2 III/ I() AO3 III/ I() AO III/ I() AO2 III/ I() AO3 III/ I() AO III/ I() AO2 III/ I() AO3 2 III/ I() AO I/ I() AO2 I/ I() AO3 I/ I() AO 2 II/9.6.8 I() AO2 2 II/ I() AO3 2 II/ I() AO I/ I() AO2 2 I/ I() AO3 2 I/ I() 29

34 Table. Perron Uni Roo Tes wih endogenous selecion of TB Model Lags Break dae ρ= CV 5% Inegraion order a 5% GDP Nominal Wages Real Wages Nom. Ineres Rae M M Growh Cons. Price Index Inflaion Real Exchange Rae Trade Balance Invesmen Paricipaion Rae Unemploymen rae Employmen Rae IO 6 IV/ I() IO2 6 IV/ I() AO2 6 I/ I() IO 3 II/ I() IO2 3 I/ I() AO2 3 IV/ I() IO 5 I/ I() IO2 5 I/ I() AO2 5 III/ I() IO 2 I/ I() IO2 IV/ I() AO2 2 III/ I() IO 3 I/ I() IO2 3 IV/ I() AO2 3 III/ I() IO 2 II/ I() IO2 2 II/ I() AO2 IV/ I() IO 3 II/ I() IO2 3 IV/ I() AO2 3 I/ I() IO 4 IV/ I() IO2 4 II/ I() AO2 I/ I() IO I/ I() IO2 5 III/ I() AO2 I/ I() IO 6 II/ I() IO2 6 II/ I() AO2 6 III/ I() IO 3 I/ I() IO2 4 IV/ I() AO2 4 IV/ I() IO I/ I() IO2 I/ I() AO2 II/ I() IO 4 I/ I() IO2 4 II/ I() AO2 4 II/ I() IO 4 II/ I() IO2 4 II/ I() AO2 4 II/ I() 3

35 Variables Augmened Dickey Fuller ρ= saisic Table. Comparaive resuls of he differen es for he Uni Roo Hypohesis Philllip Perron Z saisic Recursive Mín ADF Rolling Mín ADF Variance Raio Order of Inegraion Perron Tes for U. Roo wih Srucural Change. Exogenous selecion of TB Perron Tes for U. Roo wih Srucural Change. Endogenous selecion of TB AO AO2 AO3 IO IO2 AO2 Non weighed average GDP..% Nominal wages % Real Wages % Nominal Ineres Rae % M % M Growh % CPI % Inflaion % Real Echange Rae % Trade Balance..% Invesmen..% Paricipaion Rae % Unemploymen Rae % Employmen Rae % Coefficien of Variaion Noe: The order of inegraion derived from each es (for each variable) has been seleced comparing he observed saisics wih he % and 5% respecive criical values. A non ineger order of inegraion implies a discrepancy beween he resuls achieved wih hese criical values. For he nominal wages case in he convenional ADF es he resul of,5 indicaes ha his series is I() al 5% and I(2) a %. In he same es he,5 value for he order of inegraion of inflaion indicaes ha his variable is I() a 5% bu I() a %. The las column (Coefficien of Variaion) has been compued as he raio beween he non weighed average of he order of inegraion derived from he differen es and is sandard deviaion amongs es. 3

36 Figure 3. Recursive and Rolling esimaion of FOAC for logs, Cycle and Cycle 2 of each series A: GDP R ecursive FOAC of A Roling FO AC of A IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.8 R ecursive FO AC of A (C ycle ) Rolling FOA C A (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FO AC of A (C ycle2) Rolling FOA C of A (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A2 Roling FO AC of A2 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A2: Nominal Wages R ecursive FOAC of A2 (C ycle ) Roling FO AC of A2 (C ycle ) - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A2 (C ycle2) Roling FO AC of A2 (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A3 Roling FO AC of A3 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A3: Real Wages R ecursive FOAC of A3 (C ycle ) Roling FO AC of A3 (C ycle ) - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A3 (C ycle2) Roling FO AC of A3 (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 R ecursive FOAC of A4.9 Roling FO AC of A IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A4: Nominal Ineres Raes R ecursive FOAC of A4 (C ycle ) Roling FO AC of A4 (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.9 R ecursive FOAC of A4 (C ycle2) Roling FO AC of A4 (C ycle 2) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 32

37 Figure 3. Recursive and Rolling esimaion of FOAC for logs, Cycle and Cycle 2 of each series (Coninuaion) A5: nominal M R ecursive FOAC of A5 Roling FO AC of A5. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A5 (C ycle ) Roling FO AC of A5 (C ycle ) - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A5 (C ycle2) Roling FO AC of A5 (C ycle 2).2. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A6 Roling FOAC of A6 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A6: nominal M growh.8.6 R ecursive FOAC of A6 (C ycle ) Roling FO AC of A6 (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.9 R ecursive FOAC of A6 (C ycle2) Roling FO AC of A6 (C ycle 2) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A7 Roling FO AC of A7 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A7: CPI R ecursive FO AC of A7 (C ycle ) Rolling FO AC of A7 (C ycle ) - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A7 (C ycle2).2 Roling FO AC of A7 (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.9 R ecursive FOAC of A8 Roling FO AC of A IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A8: Inflaion.8.6 R ecursive FO AC of A8 (C ycle ) Rolling FO AC of A8 (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.9 R ecursive FOAC of A8 (C ycle2) Roling FO AC of A8 (C ycle 2) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 33

38 Figure 3. Recursive and Rolling esimaion of FOAC for logs, Cycle and Cycle 2 of each series (Coninuaion) A9: Real Exchange Rae R ecursive FOAC of A9 Roling FO AC of A9 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98.8 R ecursive FO AC of A9 (C ycle ) Rolling FO AC of A9 (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A9 (C ycle2) Roling FO AC of A9 (C ycle 2) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A Roling FO AC of A IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A: Trade balance R ecursive FO AC of A (C ycle ) Rolling FO AC of A (C ycle ) - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A (C ycle2).2 Roling FO AC of A (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A Roling FO AC of A IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A: Invesmen.8.6 R ecursive FO AC of A (C ycle ) Rolling FO AC of A (C ycle ) IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FOAC of A (C ycle2) Roling FO AC of A (C ycle 2). IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ R ecursive FO AC of B Ro ling FO AC of B I/8 3 I/8 5 I/8 7 I/8 9 I/9 I/9 3 I/9 5 I/9 7 B: Paricipaion rae.8.6 R ecursive FOAC of B (C ycle ) Roling FO AC of B (C ycle ) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/ R ecursive FOAC of B (C ycle 2) Roling FO AC of B (C ycle 2) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 34

39 Figure 3. Recursive and Rolling esimaion of FOAC for logs, Cycle and Cycle 2 of each series (Coninuaion) B2: Unemploymen rae R ecursive FO AC of B2 Ro ling FO AC of B2 I/8 3 I/8 5 I/8 7 I/8 9 I/9 I/9 3 I/9 5 I/ R ecursive FOAC of B2 (C ycle ) Roling FO AC of B2 (C ycle ) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7.9 R ecursive FOAC of B2 (C ycle 2) Roling FO AC of B2 (C ycle 2) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/ R ecursive FOAC of B3 Roling FO AC of B3 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 B3: Employmen rae.8 R ecursive FOAC of B3 (C ycle ) Roling FO AC of B3 (C ycle ) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/ R ecursive FOAC of B3 (C ycle 2) Roling FO AC of B3 (C ycle 2) II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 35

40 Figure 4. Recursive and Rolling esimaion of ADF saisic for ρ= A: GDP R ecursive ADF fo r A.5 B anerjee e all5% C.V..5.5 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 - Rolling ADF fo r A Banerjee e all5% C.V. -6 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A2: Nominal Wages 3 2 Recursive ADF fo r A2 Banerjee e all5% C.V Rolling ADF fo r A2 B anerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A3: Real Wages Recursive ADF fo r A3 Banerjee e all5% C.V IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 - Rolling ADF fo r A3 B anerjee e all5% C.V. -6 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A4: Nominal Ineres Raes Recursive ADF fo r A4 Banerjee e all5% C.V IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ Rolling ADF fo r A4 B anerjee e all5% C.V. - 8 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 36

41 Figure 4. Recursive and Rolling esimaion of ADF saisic for ρ= (coninuaion) A5: nominal M 2 - Recursive ADF fo r A5 Banerjee e all5% C.V Rolling ADF fo r A5 B anerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A6: nominal M growh 5 4 Recursive ADF fo r A6 3 2 Banerjee e all5% C.V. - IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ Rolling ADF fo r A6 B anerjee e all5% C.V. - 2 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ Recursive ADF fo r A7 Banerjee e all5% C.V. 5 - A7: CPI Rolling ADF fo r A7 B anerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A8: Inflaion 5 - Recursive ADF fo r A8 Banerjee e all5% C.V Rolling ADF fo r A8 B anerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 37

42 Figure 4. Recursive and Rolling esimaion of ADF saisic for ρ= (coninuaion) A9: Real Exchange Rae Recursive ADF fo r A9 Banerjee e all5% C.V IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/ Rolling ADF fo r A9 B anerjee e all5% C.V. -9 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A: Trade balance Recursive ADF fo r A Banerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 - Rolling ADF fo r A B anerjee e all5% C.V. -6 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 A: Invesmen R ecursive ADF fo r A B anerjee e all5% C.V. IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 - Rolling ADF fo r A B anerjee e all5% C.V. -6 IV/86 IV/88 IV/9 IV/92 IV/94 IV/96 IV/98 B: Paricipaion rae Recursive ADF fo r B.5 Banerjee e all5% C.V..5.5 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 - Rolling ADF fo r B Banerjee e all5% C.V. -6 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 38

43 Figure 4. Recursive and Rolling esimaion of ADF saisic for ρ= (coninuaion) B2: Unemploymen rae 2 - R ecursive ADF fo r B2 B anerjee e all5% C.V. - Rolling ADF fo r B2 B anerjee e all5% C.V. -6 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7-7 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/ R ecursive ADF fo r B3 B anerjee e all5% C.V. B3: Employmen rae II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 Rolling ADF fo r B3 B anerjee e all5% C.V. -6 II/8 3 II/8 5 II/8 7 II/8 9 II/9 II/9 3 II/9 5 II/9 7 39